Given a function whose body is a lambda, you can use the function syntactic sugar to move the lambda arguments to the left of the = sign. One side condition is that you can't have a where binding, for example:

function x = \y -> xx + y
where xx = trace "hit" x

This is equivalent to:

function x = let xx = trace "hit" x in \y -> xx + y

Moving a let under a lambda can cause arbitrary additional computation, as I previously described, so is not allowed (hint: think of map (function 1) [2..5]).

View Patterns

One side condition I hadn't anticipated is that if x is a view pattern, the transformation can still reduce sharing. Consider:

function (trace "hit" -> xx) = \y -> xx + y

This is equivalent to:

function x = case trace "hit" x of xx -> \y -> xx + y

And moving y to the right of the = causes trace "hit" to be recomputed for every value of y.

I've now fixed HLint 1.9.22 to spot this case. Using Uniplate, I added the side condition:

null (universeBi pats :: [Exp_])

Specifically, there must be no expressions inside the pattern, which covers the PViewPat constructor, and any others that might harbour expressions (and thus computation) in future.

The problem with function definitions also applies equally to \p1 -> \p2 -> e, which cannot be safely rewritten as \p1 p2 -> e if p1 contains a view pattern.

The Problem Worsens (Pattern Synonyms)

Pattern synonyms make this problem worse, as they can embody arbitrary computation in a pattern, which is lexically indistinguishable from a normal constructor. As an example:

pattern Odd <- (odd -> True)
f Odd = 1
f _ = 2

However, putting complex computation behind a pattern is probably not a good idea, since it makes it harder for the programmer to understand the performance characteristics. You could also argue that using view patterns and lambda expressions to capture computation after partial application on definitions then lambda expressions is also confusing, so I've refactored Shake to avoid that.

Potential Fixes

I think it should be possible to fix the problem by optimising the desugaring of functions, ensuring patterns are matched left-to-right where allowable, and that each match happens before the lambda requesting the next argument. The question is whether such a change would improve performance generally. Let's take an example:

Which goes 3-4x faster when running map (test [1..]) [1..n] at -O2 (thanks to Jorge Acereda Maciá for the benchmarks). The trace is required to avoid GHC deoptimising the second variant to the first, as per GHC bug #11029.

There are two main downsides I can think of. Firstly, the desugaring becomes more complex. Secondly, these extra lambdas introduce overhead, as the STG machine GHC uses makes multiple argument lambdas cheaper. That overhead could be removed using call-site analysis and other optimisations, so those optimisations might need improving before this optimisation produces a general benefit.

Monday, October 26, 2015

Summary: When thinking about the filepath .., remember symlinks, or you will trip yourself up.

As the maintainer of the Haskell filepath package, one common path-related mistake I see is the assumption that filepaths have the invariant:

/bob/home/../cookies == /bob/cookies

I can see the conceptual appeal - go down one directory, go up one directory, end up where you started. Unfortunately, it's not true. Consider the case where home is a symlink to tony/home. Now, applying the symlink leaves us with the case:

/tony/home/../cookies == /bob/cookies

And, assuming /tony/home is itself not a symlink, that reduces to:

/tony/cookies == /bob/cookies

This is clearly incorrect (assuming no symlinks), so the original invariant was also incorrect, and cannot be relied upon in general. The subtle bit is that descending into a directory might move somewhere else, so it's not an operation that can be undone with ... Each step of the path is interpreted based on where it ends up, not based on the path it took to the current point.

While this property isn't true in general, there are many special cases where it is reasonable to assume. For example, the shake package contains a normaliseEx function that normalises under this assumption, but nothing in the standard filepath package assumes it.

This Shake talk took a distinct approach from my previous talks - partly because I now have a better understanding of how large Shake build systems are typically structured. The key theoretical innovation of Shake is monadic dependencies, and the key technical innovation is using Haskell as an embedded language. Putting these pieces together lets Shake users write a build system interpreter, rather than a monolithic build system.

In the talk I suggest that build systems can be split into metadata (changes frequently, can be tracked, custom format for each project relying on conventions) and an interpreter for that metadata (written using Shake). The result seems to work quite nicely, especially in larger projects where everyone is expected to update the metadata, but changes to the interpreter are expected to be rarer and more carefully thought out.

One of the goals of the talk was to convert some of the audience to using Shake. It seems to have worked, as @krisajenkinstweeted:

First fruit of #haskellx - switched my makefiles over to Shake. Parallelised builds & a readable syntax. Much win.